1. Field of the Invention
This invention relates to a method for controlling pH in a continuous flow vessel which is entered by a process material through a feed channel and by controlling chemical solution through a control channel and in which the pH is measured at the output part of the vessel in order to effect the control by controlling the feed of the control chemical by the feedback method, the value of a reference variable being given and expressed by a pH number. The invention also concerns an apparatus for carrying out such method.
2. Description of the Prior Art
The control of acidity belongs to the most common control tasks in industry, acquisition of water and treatment of waste liquids. For its normal ways of realization, it is comparable with the control of other common process variables. pH which is a quantity descriptive of the acidity is measured by a pH meter or transmitter, and the output signal from this is brought immediately to the comparator of the controller which provides the control for the feed of the controlling chemical to the feed channel or to later point of the process. The difficulties appearing in the pH control are, however, greater than those in the control of other process variables. As reasons for this are mentioned i.a. nonlinearity present in the control loop and high sensitivity of the process.
As a physical phenomenon, the acidity or pH of a water solution is determined by the concentrations of the dissolved chemicals. In the case of pure liquids the dissociation equilibrium is reached fast and the state of the process can be expressed by means of algebraic equilibrium equations by which the hydrogen ion concentration or acidity can be unambiguously determined.
In order to set up the dynamic model, the above equilibrium model has to be added to the dynamic flow model of the process. Starting from the known, simple model of the continuous flow ideal mixer either as such or combined with a plug flow such reactor model has been set up and, using it, the feedback control simulated (Richter & al., Instrumentation Technology, 21, No. 4, p. 35-40, 1974), optimal control (McAvoy, Ind., & Eng. Chem., Process Des. & Develop., 11, No. 1, p. 71-78, 1972) and stability studied (Orava & Niemi, Int. of Control, 20, No. 4, p. 557-567, 1974. Rang, Advances in Instrumentation, 30, Part 3, p. 764/1-4, 1975).
Conclusions on how models based on the thermodynamic equilibrium can be applied to the practical pH control, have not been brought to the level of an industrial exploitation; i.e. up to now no clear suggestion has been made on such feedback control loop for pH which using actions based on models would yield a better result than the pH control by conventional, previously known methods.
ph process.
While the model of the hydrogen ion concentration is formulated, the liquid is assumed homogeneous and the appearing dissociation processes fast and reversible. These assumptions are valid both for strong or fully dissociating and weak or partly dissociating acids and bases. The acidity under these conditions has been treated thoroughly i.a. in the U.S. Pat. No. 4,053,743 granted to A. Niemi. The equilibrium dependences of the dissociation processes can also be combined in one algebraic equation shown below (Rang, loc. cit.). The activities have been substituted here by the concentrations and the coefficients K.sub.aj and K.sub.bi describe the dissociation of weak acids and bases. K.sub.w is the ion product of water at 25.degree. C. ##EQU1## C.sup.+ concentration of H.sup.+ ion C.sup.- concentration of OH.sup.- ion
C.sub.A concentration of strong acid PA1 C.sub.B concentration of strong base PA1 C.sub..alpha. concentration of weak acid PA1 C.sub..beta. concentration of weak base PA1 C.sub.a concentration of undissociated acid PA1 C.sub.b concentration of undissociated base PA1 C.sub.a.sup.- concentration of weak anion PA1 C.sub.b.sup.+ concentration of weak cation
The two first terms of the equation (1) express the difference of the concentrations of the hydrogen and hydroxyl ions. If only strong acids are present, this quantity depends linearly and unambiguously on the concentration difference of the strong acids and bases present.
Since the process of mixing of homogeneous solutions is linear with regard to the concentration, the total process is linear also with regard to such chemicals for which the dissociation may be left inconsidered at the determination of their concentrations. The concentration, at the process output, of a chemical fed to the process, can then be determined in the general case by means of the convolution integral, if the weighting function of the process is known which in this case is identical with the residence time distribution. If e.g. a process solution containing a weak acid (weighting function g.sub.o) and a control solution containing a strong base, through the control channel, (weighting function g.sub.1) are fed to a continuous flow vessel, the following process model is obtained for their total concentrations: ##EQU2## 0, 1 as subindices refer to process feed flow and control flow, respectively.
The dependence of the concentration of the hydrogen ion C.sup.+ on the concentrations of the weak acid and strong base is obtained from Eq. (1) (n=0, m=1, C.sub.A =0): EQU C.sup.+3 +(C.sub.B +K.sub.a)C.sup.+2 +(K.sub.a C.sub.B -K.sub.a C.sub..alpha. -K.sub.a K.sub.w =0 (5)
The equations (4) and (5) form in this case a complete model of the system. Also in this case, the state of the system can be described by linear equations, but due to the presence of the weak compound the output relationship (5) is non-linear with regard to C.sup.+.
The pH value indicating the acidity of the solution is measured by a suitable pair of electrodes followed by a linear amplifier. The voltage from the electrodes bears, on its part, a linear relation to the pH value of the solution which is a non-linear function of the hydrogen ion concentration. EQU pH=-log.sub.10 [C.sup.+ /mole/liter)] (6)